On the auxetic properties of rotating rhombi and parallelograms : a preliminary investigation

Abstract

Auxetics exhibit the unusual property of expanding when uniaxially stretched (negative Poisson's ratio), a property that is usually linked to particular geometric features and deformation mechanisms. One of the mechanisms which results in auxetic behaviour is the one involving rotating rigid units, for which, systems made from triangles, squares or rectangles have already been considered. In this work we extend this study by considering systems which can be constructed from either connected rhombi or connected parallelograms. We show that various types of such systems can exist and we discuss in detail the properties of one type of ‘rotating rhombi' and one type of ‘rotating parallelograms'. We also show that the Poisson's ratio of these systems, which can be positive or negative, is anisotropic and dependent on the shape of the parallelograms/rhombi and the degree of openness of the system.